# Physical Scaling of Oil Production Rates and Ultimate Recovery from All Horizontal Wells in the Bakken Shale

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Physical Scaling

#### 2.1.1. Physical Scaling of Natural Depletion

#### 2.1.2. Physical Scaling of Well Refracturing

#### 2.2. Data Collection and Scaling Procedure

- Exclude all newly completed wells with less than 12 months of production.
- For each remaining well, plot its cumulative production vs. square root of time on production. Classify these wells as:
- (a)
- Non-interfering wells, if the plot shows a straight line (with, e.g., ${\mathrm{R}}^{2}\ge 0.9$).
- (b)
- Interfering wells, if the plot shows a deviation from a straight line (with, e.g., ${\mathrm{R}}^{2}<0.9$)
- (c)
- Refrac wells, if production jumps are detected.

- For each non-interfering well, scale its cumulative production by $\mathcal{K}\sqrt{{t}_{max}}$, on the $y-$axis and the elapsed time on production by ${t}_{max}$ on the $x-$axis to match the line $f\left(\tilde{t}\right)=\sqrt{\tilde{t}}$. To predict EUR, assume that deviation from the line starts at $\tau =2{t}_{max}$. Thus, the corresponding $\mathcal{M}$ can be calculated as $\mathcal{M}=\left(\mathcal{K}\sqrt{{t}_{max}}\right)/\mathrm{RF}\left(\frac{1}{2}\right)$, where $\mathrm{RF}\left(\frac{1}{2}\right)$ is calculated from Equation (8). Finally, $\mathrm{EUR}$ is calculated from Equation (11).
- For each newly completed well, calculate its EUR using expected values of $\tau $ and $\mathcal{M}$ from comparable interfering wells that were completed between 2017 and 2019. Use Equation (11).

## 3. Results and Discussion

#### 3.1. Physical Scaling Matches

#### 3.2. EUR Predictions

^{®}program to automate the hyperbolic DCA matches of 14,888 Bakken oil wells. Figure 10a,b are examples of the respective matches of oil production from well -25-083-XXXXX. The rate is plotted on a semilog scale and there seem to be no large discrepancies between the physical scaling (blue curve) and hyperbolic DCA (red curve) matches of the past oil rate (black line). However, when we integrate the rate estimates from both methods to obtain cumulative production, the hyperbolic DCA fails to trace past production and gives an overly optimistic cumulative oil of 64,000 m${}^{3}$ (400 kbbl) at the last production time recorded. In contrast, the physical scaling yields 55,600 m${}^{3}$ (350 kbbl) matching exactly historical data. We also quality-checked both methods for 11,246 non-refractured wells in the Bakken, see Figure 10c,d. For each well, each point in these cross-plots quantifies agreement between the actual annual rate (the volume of oil produced during 12 months on production in kbbl/year), in year $1,2,\dots $, and the corresponding values predicted with both methods. There are 61,230 points in each of the two cross-plots. Ideally, these points would follow the diagonal line, $y=x$. For DCA, best data fit, $y=1.12x+1.14$, (the blue line) is biased towards excessive predicted production volumes. The linear model explains the data almost perfectly and its 95% confidence interval (CI) is not plotted. The two dashed blue lines denote the 95% CI band that a new data point in the same set of wells would fall inside of this band. The physical scaling model is not biased, $y=0.99x-0.13$, and its 95% CI is narrower. Finally, we stacked up all rate estimates from the 14,888 oil wells in the Bakken to obtain total field rate shown in Figure 10e. At the field scale, the systematic upward bias of hyperbolic DCA is amplified, thus, the red line fails to track the black line. In contrast, the stack of individual physical scaling matches (blue line) traces historical production. The total field cumulative is shown in Figure 10f. In the end, there is a big discrepancy between both methods of predicting total field EUR from the same field production data set. The physical scaling predicts the EUR from the 14,888 existing wells at 715 million m${}^{3}$ (4.5 billion bbl), while the hyperbolic DCA is overly optimistic, giving a 45% higher estimate of 1 billion m${}^{3}$ (6.5 billion bbl).

## 4. Conclusions

- The current 14,888 active oil wells in the Bakken shale will ultimately produce 715 million m${}^{3}$ (4.5 billion barrels) of oil, with 493 million m${}^{3}$ (3.1 billion barrels) from 9894 wells in the Middle Bakken and 222 million m${}^{3}$ (1.4 billion barrels) from 4994 wells in the Upper Three Forks.
- In general, wells completed in the Middle Bakken produce more oil than those in the Upper Three Forks due to: (1) lower water saturation and water cut, (2) slower decline rate (longer pressure interference times, $\tau $), and (3) higher initial oil in place (larger $\mathcal{M}$).
- Newly completed wells start from very high initial oil rates but in general decline faster than the pre-2010 wells. Still, we predict higher EURs for the newly completed wells.
- The more productive newer wells result from recent advancements in completion technology: longer laterals, larger hydrofractures, bigger stimulated reservoir volumes, and more fracture stages.
- Operators have also learned to drill new wells only in the most prolific area of the Bakken region at the center of the Williston Basin.
- With time, negative trends in oil production have amplified in the Bakken. We observe higher GOR values (reservoir degassing); higher water cuts (contacting water-bearing formations and drilling in regions with lower oil saturations); faster decline rates; and excessive well density, especially in the most prolific areas.
- When all most productive areas in the Bakken are extensively drilled, the poor immature areas with high water production will be the only targets left for infill drilling. In this case, technology will not enhance much performance of the future wells.
- We encourage practitioners to adopt our fast and accurate method of predicting oil production in shales that is a viable alternative to the hyperbolic DCA which yields an ‘illusory picture’ of shale oil resources.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

${a}_{j}$ | effectiveness of a refrac job |

${A}_{f}$ | one-sided area of hydrofracture, ft${}^{2}$ [m${}^{2}$] |

${c}_{o}$ | oil compressibility, psi${}^{-1}$ [Mpa${}^{-1}$] |

${c}_{w}$ | water compressibility, psi${}^{-1}$ [Mpa${}^{-1}$] |

${c}_{\varphi}$ | pore space compressibility, psi${}^{-1}$ [Mpa${}^{-1}$] |

${c}_{t}$ | total compressibility, psi${}^{-1}$ [Mpa${}^{-1}$] |

C | maximum recovery factor before refracturing, fraction |

d | half-distance between two consecutive hydrofractures, ft [m] |

$\mathrm{EUR}$ | estimated ultimate recovery of oil, million bbl, Mbbl |

${\mathrm{EUR}}_{\mathrm{T}}$ | total estimated ultimate recovery of oil from a refractured well, million bbl, Mbbl |

$\mathrm{GOR}$ | dissolved gas–oil ratio, scf/stb [sm${}^{3}$/m${}^{3}$] |

H | fracture height, assumed equal to formation thickness, ft [m] |

${\mathbb{H}}_{j}$ | Heaviside unit step function |

i | the ${i}^{th}$ month on production |

j | the ${j}^{th}$ discontinuity of production rate from a refracturing event |

k | average permeability of the matrix, $\mu $d [m${}^{2}$] |

$\mathcal{K}$ | dimensional scaling constant, kton/$\sqrt{\mathrm{month}}$ |

L | hydrofracture half-length, ft [m] |

$\mathcal{M}$ | mass of saturated oil inside stimulated reservoir volume, kton |

${\mathcal{M}}_{0}$ | mass of saturated oil inside stimulated reservoir volume before refracturing, kton |

${\mathcal{M}}_{j}$ | mass of saturated oil inside stimulated reservoir volume after j^{th} refracturing, kton |

N | total number of parallel vertical hydrofractures in a well |

${N}_{p}$ | cumulative mass production of oil, kton |

p | pressure, psi [Mpa] |

${p}_{i}$ | estimated initial formation pressure, psi [Mpa] |

${p}_{b}$ | average bubble point pressure, psi [Mpa] |

${p}_{f}$ | constant pressure in hydrofractures, psi [Mpa] |

${P}_{x}$ | a number such that there is an $x\%$ likelihood that true value exceeds ${P}_{x}$ |

q | oil production rate at downhole conditions, bbl/day [m${}^{3}$/s] |

${q}_{ST}$ | oil production rate at stock tank conditions, bbl/day [m${}^{3}$/s] |

${\mathrm{R}}^{2}$ | a statistical measure of how close the data are to the fitted regression curve |

${q}_{\mathrm{field},\mathrm{ST}}$ | volume of oil produced in month i by a horizontal well, stb/month |

$\mathrm{RF}$ | recovery factor, fraction |

${\mathrm{RF}}_{j}$ | recovery factor for an imaginary well due to j^{th} refracturing event, fraction |

${\mathrm{RF}}_{\mathrm{T}}$ | total recovery factor for a refractured well, fraction |

${R}_{s}$ | solution gas–oil ratio, scf/stb [sm${}^{3}$/m${}^{3}$] |

${S}_{oi}$ | initial oil saturation |

${S}_{wc}$ | connate water saturation |

t | elapsed time on production, months [s] |

${t}_{j}$ | elapsed time when j^{th} refracturing event occurs, months [s] |

$\tilde{t}$ | dimensionless time |

x | distance, ft [m] |

$\alpha $ | pressure diffusivity coefficient, m${}^{2}$/s |

${\alpha}_{i}$ | pressure diffusivity coefficient at initial conditions, m${}^{2}$/s |

$\beta $ | exponent constant in simplified master curve equation |

$\lambda $ | Conway’s constant ≈ 1.30357 |

${\mu}_{o}$ | oil viscosity, cp [Pa s] |

${\mu}_{oi}$ | oil viscosity at initial conditions, cp [Pa s] |

${\rho}_{\mathrm{fluid},i}$ | fluid density at initial conditions, lb/ft${}^{3}$ [kg/m${}^{3}$] |

${\rho}_{g,\mathrm{ST}}$ | gas density at stock tank conditions, lb/ft${}^{3}$ [kg/m${}^{3}$] |

${\rho}_{o}$ | oil density, lb/ft${}^{3}$ [kg/m${}^{3}$] |

${\rho}_{oi}$ | oil density at initial conditions, lb/ft${}^{3}$ [kg/m${}^{3}$] |

${\rho}_{\mathrm{ST}}$ | oil density at stock tank (dead oil) conditions, lb/ft${}^{3}$ [kg/m${}^{3}$] |

${\rho}_{w}$ | water density, lb/ft${}^{3}$ [kg/m${}^{3}$] |

$\varphi $ | porosity, fraction |

$\tau $ | characteristic pressure interference time, months |

## Appendix A. Overview of the Bakken Shale Play

**Figure A2.**Bakken well log data of well-33-055-XXXXX (

**a**) and well-33-053-XXXXX (

**b**) from the North Dakota Department of Mineral Resources—Oil and Gas Division home page.

**Table A1.**The average reservoir properties from well log data shown in Figure A2.

Formation | Upper Bakken | Middle Bakken | Lower Bakken | Upper Three Forks |
---|---|---|---|---|

Depth (m) | 3108 | 3116 | 3125 | 3136 |

Pressure (Mpa) | 36.7 | 36.8 | 36.9 | 37.0 |

Temperature ($\xb0$C) | 103 | 103 | 104 | 104 |

Gamma-Ray ($\xb0$ API) | 431 | 83 | 690 | 81 |

Permeability (m${}^{2}$) | 1.4 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-19}$ | 4.5 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-17}$ | 2.0 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-19}$ | 4.7 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-17}$ |

Porosity | 0.008 | 0.046 | 0.008 | 0.058 |

Water Saturation | 0.20 | 0.57 | 0.22 | 0.65 |

Thickness (m) | 5.8 | 10 | 9.1 | 12 |

**Figure A3.**Maps of gas–oil ratio (

**a**) and water cut (

**b**) for all horizontal oil wells in the Middle Bakken and the Upper Three Forks. The colored labels and line borders represent the five assessment units: Central Basin (CB), Eastern Transitional (ET), Nesson-Little Knife (NL), and Northwest Transitional (NT).

## Appendix B. Bakken Reservoir Properties, Summary of Matching Parameters, and Details of EURs

**Table A2.**Reservoir properties used in scaling oil production in the Middle Bakken and Upper Three Forks.

Parameter | Middle Bakken | Upper Three Forks | Data Source | ||
---|---|---|---|---|---|

SI Units | Field Units | SI Units | Field Units | ||

Horizontal well length, ${L}_{w}$ | 2900 m | 9500 ft | 2900 m | 9500 ft | DrillingInfo |

Number of fracture stages, N | 30 | 30 | 30 | 30 | DrillingInfo |

Fracture height, H | 10 m | 33 ft | 12 m | 40 ft | well log |

Tip-to-tip fracture length, $2L$ | 360 m | 1200 ft | 360 m | 1200 ft | DrillingInfo |

Reservoir temperature, T | 113 $\xb0$C | 237 $\xb0$F | 115 $\xb0$C | 239 $\xb0$F | [65] |

Initial pressure, ${p}_{i}$ | 36.8 Mpa | 5340 psia | 37.1 Mpa | 5380 psia | well log |

Saturation pressure, ${p}_{b}$ | 17.4 Mpa | 2530 psia | 12.1 Mpa | 1753 psia | [65] |

Fracture pressure, ${p}_{f}$ | 3.4 Mpa | 500 psia | 3.4 Mpa | 500 psia | DrillingInfo |

Connate water saturation, ${S}_{wc}$ | 0.57 | 0.57 | 0.65 | 0.65 | well log |

Initial oil saturation, ${S}_{oi}$ | 0.43 | 0.43 | 0.35 | 0.35 | well log |

Rock porosity, $\varphi $ | 0.046 | 0.046 | 0.058 | 0.058 | well log |

Rock permeability, k | 4.4 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-17}$ m${}^{2}$ | 0.045 md | 4.6 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-17}$ m${}^{2}$ | 0.047 md | well log |

Rock compressibility, ${c}_{\varphi}$ | 4.3 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-10}$ Pa${}^{-1}$ | 3.0 microsip | 4.3 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-10}$ Pa${}^{-1}$ | 3 microsip | [66] |

Water compressibility, ${c}_{w}$ | 4.3 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-10}$ Pa${}^{-1}$ | 3 microsip | 4.3 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-10}$ Pa${}^{-1}$ | 3 microsip | [66] |

Oil compressibility, ${c}_{o}$ | 1.4 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ Pa${}^{-1}$ | 1 microsip | 1.4 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-9}$ Pa${}^{-1}$ | 1 microsip | [66] |

Oil viscosity, ${\mu}_{oi}$ | 3.9 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$ Pa s | 0.392 cp | 2.8 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$ Pa s | 0.276 cp | [65] |

Oil formation volume factor, ${B}_{oi}$ | 1.61 m${}^{3}$/sm${}^{3}$ | 1.61 rbbl/stb | 1.48 m${}^{3}$/sm${}^{3}$ | 1.48 rbbl/stb | [65] |

API gravity | 42 $\xb0$ API | 42 $\xb0$ API | 39 $\xb0$ API | 39 $\xb0$ API | [65] |

GOR | 1.48 sm${}^{3}$/sm${}^{3}$ | 125 scf/stb | 110 sm${}^{3}$/sm${}^{3}$ | 620 scf/stb | [65] |

**Table A3.**Summary of pressure interference time, $\tau $, and mass of oil in place, $\mathcal{M}$, for four different well classes in the Middle Bakken and Upper Three Forks.

Well Class | Middle Bakken | Upper Three Forks | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathit{\tau}$ (months) | $\mathcal{M}$ (ktons) | Number | $\mathit{\tau}$ (months) | $\mathcal{M}$ (ktons) | Number | |||||||||

${\mathit{P}}_{10}$ | ${\mathit{P}}_{50}$ | ${\mathit{P}}_{90}$ | ${\mathit{P}}_{10}$ | ${\mathit{P}}_{50}$ | ${\mathit{P}}_{90}$ | of Wells | ${\mathit{P}}_{10}$ | ${\mathit{P}}_{50}$ | ${\mathit{P}}_{90}$ | ${\mathit{P}}_{10}$ | ${\mathit{P}}_{50}$ | ${\mathit{P}}_{90}$ | of Wells | |

Interfering | 170 | 100 | 50 | 720 | 420 | 190 | 4245 | 140 | 90 | 40 | 540 | 320 | 150 | 2156 |

Non-Interfering | 250 | 220 | 180 | 860 | 480 | 250 | 3349 | 250 | 210 | 160 | 680 | 400 | 170 | 1496 |

Refracs | 230 | 150 | 70 | 1210 | 660 | 230 | 1549 | 230 | 140 | 70 | 980 | 540 | 200 | 814 |

Newly completed | 60 | 50 | 30 | 800 | 520 | 270 | 751 | 60 | 40 | 30 | 620 | 400 | 200 | 528 |

All wells | 200 | 150 | 90 | 850 | 490 | 220 | 9894 | 180 | 130 | 80 | 660 | 390 | 170 | 4994 |

AU | State | County | EIA 2019 | Physical Scaling | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Bakken | Three Forks | Bakken | Three Forks | |||||||||||

EUR | Potential | EUR | Potential | P10 | P50 | P90 | Existing | P10 | P50 | P90 | Existing | |||

(Mb/well) | wells | (Mb/well) | wells | (Mb/well) | (Mb/well) | (Mb/well) | wells | (Mb/well) | (Mb/well) | (Mb/well) | wells | |||

Central Basin | MT | Daniels | 60 | 189 | 177 | 35,870 | - | - | - | - | - | - | - | - |

Central Basin | MT | McCone | 60 | 528 | 196 | 196 | 196 | 1 | - | - | - | - | ||

Central Basin | MT | Richland | 232 | 1083 | 318 | 210 | 103 | 102 | 234 | 118 | 44 | 3 | ||

Central Basin | MT | Roosevelt | 263 | 4985 | 330 | 212 | 103 | 138 | 228 | 129 | 38 | 11 | ||

Central Basin | MT | Sheridan | 49 | 753 | 359 | 163 | 37 | 4 | 64 | 59 | 53 | 2 | ||

Central Basin | ND | Divide | 241 | 12 | - | - | - | - | 99 | -307 | 27 | 3 | ||

Central Basin | ND | Dunn | 184 | 73 | 459 | 301 | 156 | 41 | 375 | 254 | 160 | 14 | ||

Central Basin | ND | McKenzie | 263 | 3749 | 465 | 298 | 158 | 1540 | 399 | 250 | 125 | 669 | ||

Central Basin | ND | Williams | 262 | 3070 | 463 | 300 | 162 | 1261 | 376 | 250 | 143 | 524 | ||

Eastern Transitional | ND | Burke | 7 | 2706 | 267 | 153 | 62 | 117 | 235 | 148 | 81 | 24 | ||

Eastern Transitional | ND | Divide | 140 | 658 | 237 | 140 | 64 | 96 | 311 | 182 | 78 | 206 | ||

Eastern Transitional | ND | Dunn | 423 | 1099 | 620 | 354 | 125 | 248 | 554 | 335 | 208 | 111 | ||

Eastern Transitional | ND | Hettinger | 169 | 7 | - | - | - | - | - | - | - | - | ||

Eastern Transitional | ND | McLean | 623 | 245 | 523 | 310 | 144 | 40 | 1198 | 501 | 193 | 4 | ||

Eastern Transitional | ND | Mercer | 13 | 144 | - | - | - | - | - | - | - | - | ||

Eastern Transitional | ND | Mountrail | 232 | 2679 | 683 | 388 | 155 | 1163 | 464 | 274 | 114 | 201 | ||

Eastern Transitional | ND | Stark | 169 | 371 | 177 | 177 | 177 | 1 | 125 | 21 | 11 | 2 | ||

Eastern Transitional | ND | Ward | 80 | 111 | 209 | 209 | 209 | 1 | - | - | - | - | ||

Elm Coulee–Billings Nose | MT | McCone | 80 | 116 | - | - | - | - | - | - | - | - | ||

Elm Coulee–Billings Nose | MT | Richland | 183 | 3421 | 423 | 230 | 75 | 935 | 112 | 64 | 15 | 2 | ||

Elm Coulee–Billings Nose | ND | Billings | 60 | 828 | 263 | 192 | 17 | 10 | 265 | 149 | 59 | 37 | ||

Elm Coulee–Billings Nose | ND | Golden Valley | 476 | 130 | 70 | 70 | 70 | 1 | 502 | 337 | 172 | 12 | ||

Elm Coulee–Billings Nose | ND | McKenzie | 184 | 2449 | 269 | 157 | 62 | 79 | 291 | 134 | 9 | 8 | ||

Nesson–Little Knife | ND | Billings | 167 | 586 | 268 | 135 | 31 | 49 | 280 | 165 | 76 | 82 | ||

Nesson–Little Knife | ND | Burke | 188 | 680 | 258 | 174 | 95 | 65 | 265 | 173 | 91 | 68 | ||

Nesson–Little Knife | ND | Divide | 115 | 603 | 246 | 159 | 82 | 128 | 236 | 151 | 77 | 149 | ||

Nesson–Little Knife | ND | Dunn | 324 | 2685 | 615 | 358 | 185 | 1258 | 569 | 345 | 181 | 608 | ||

Nesson–Little Knife | ND | Hettinger | 223 | 106 | - | - | - | - | - | - | - | - | ||

Nesson–Little Knife | ND | McKenzie | 329 | 1520 | 651 | 397 | 200 | 1072 | 610 | 362 | 164 | 1006 | ||

Nesson–Little Knife | ND | Mountrail | 312 | 530 | 545 | 326 | 147 | 975 | 503 | 304 | 146 | 655 | ||

Nesson–Little Knife | ND | Slope | 120 | 167 | - | - | - | - | - | - | - | - | ||

Nesson–Little Knife | ND | Stark | 156 | 2164 | 199 | 167 | 134 | 2 | 343 | 203 | 93 | 219 | ||

Nesson–Little Knife | ND | Williams | 178 | 1828 | 365 | 213 | 96 | 410 | 349 | 211 | 100 | 243 | ||

Northwest–Transitional | MT | Daniels | 82 | 2584 | - | - | - | - | - | - | - | - | ||

Northwest–Transitional | MT | McCone | 82 | 161 | - | - | - | - | - | - | - | - | ||

Northwest–Transitional | MT | Roosevelt | 82 | 1312 | - | - | - | - | - | - | - | - | ||

Northwest–Transitional | MT | Sheridan | 50 | 2857 | 195 | 100 | 24 | 27 | 67 | 67 | 67 | 1 | ||

Northwest–Transitional | MT | Valley | 1 | 1005 | - | - | - | - | - | - | - | - | ||

Northwest–Transitional | ND | Divide | 180 | 601 | 248 | 158 | 87 | 41 | 239 | 153 | 77 | 110 | ||

Northwest–Transitional | ND | Williams | 212 | 669 | 311 | 185 | 81 | 89 | 317 | 224 | 85 | 20 | ||

AVERAGE EUR (thousand bbl) | 189 | 177 | 515 | 309 | 146 | 456 | 278 | 136 | ||||||

TOTAL WELL | 49,464 | 35,870 | 9894 | 4994 | ||||||||||

TOTAL EUR (billion bbl) | 9.3 | 6.3 | 5.1 | 3.1 | 1.4 | 2.3 | 1.4 | 0.7 |

## References

- Medeiros, F.; Ozkan, E.; Kazemi, H. Productivity and Drainage Area of Fractured Horizontal Wells in Tight Gas Reservoirs. In Proceedings of the Rocky Mountain Oil & Gas Technology Symposium, Denver, CO, USA, 16–18 April 2007. [Google Scholar]
- Ikonnikova, S.; Browning, J.; Horvath, S.C.; Tinker, S. Well Recovery, Drainage Area, and Future Drill-Well Inventory: Empirical Study of the Barnett Shale Gas Play. SPE Res. Eval. Eng.
**2014**, 17, 484–496. [Google Scholar] [CrossRef] - Arps, J. Analysis of Decline Curves. Trans. AIME
**1945**, 160, 228–247. [Google Scholar] [CrossRef] - Gaswirth, S.B.; Marra, K.R.; Cook, T.A.; Charpentier, R.R.; Gautier, D.L.; Higley, D.K.; Klett, T.R.; Lewan, M.D.; Lillis, P.G.; Schenk, C.J. Assessment of undiscovered oil resources in the bakken and three forks formations, Williston Basin Province, Montana, North Dakota, and South Dakota, 2013. US Geol. Surv. Fact Sheet
**2013**, 3013, 1–4. [Google Scholar] - Cook, T.A. Procedure for Calculating Estimated Ultimate Recoveries of Bakken and Three Forks Formations Horizontal Wells in the Williston Basin; US Geol. Surv. Open-File Report; U.S. Geological Survey: Reston, VA, USA, 2013; pp. 1–14. [Google Scholar]
- EIA. Assumptions to the Annual Energy Outlook 2019: Oil and Gas Supply Module. US Energy Inf. Adm. Ann. Energy Outlook
**2019**, 7, 4–7. [Google Scholar] - Kanfar, M.; Wattenbarger, R. Comparison of Empirical Decline Curve Methods for Shale Wells. In Proceedings of the SPE Canadian Unconventional Resources Conference, Calgary, AB, Canada, 30 October–1 November 2012. [Google Scholar]
- Tan, L.; Zuo, L.; Wang, B. Methods of Decline Curve Analysis for Shale Gas Reservoirs. Energies
**2018**, 11, 552. [Google Scholar] [CrossRef] [Green Version] - Olson, B.; Elliott, R.; Mathhews, C.M. Fracking’s Secret Problem–Oil Wells Aren’t Producing as Much as Forecast. The Wall Street Journal, 2 January 2019. Available online: https://www.wsj.com/articles/frackings-secret-problemoil-wells-arent-producing-as-much-as-forecast-11546450162(accessed on 27 October 2019).
- Lapierre, S. On the Nature and Character of the Widespread Oil Production Shortfalls Reported by the Wall Street Journal. Linkedin Pulse, 11 September 2019. Available online: https://www.linkedin.com/pulse/nature-character-widespread-oil-production-shortfalls-scott-lapierre(accessed on 27 October 2019).
- Ilk, D.; Rushing, J.A.; Perego, A.D.; Blasingame, T.A. Exponential vs. Hyperbolic Decline in Tight Gas Sands: Understanding the Origin and Implications for Reserve Estimates Using Arps & Decline Curves. In Proceedings of the SPE Annual Technical Conference and Exhibition, Denver, CO, USA, 21–24 September 2008. [Google Scholar]
- Valko, P.P. Assigning value to stimulation in the Barnett Shale: A simultaneous analysis of 7000 plus production hystories and well completion records. In Proceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 19-21 January 2009. [Google Scholar]
- Valko, P.P.; Lee, W.J. A Better Way To Forecast Production From Unconventional Gas Wells. In Proceedings of the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September 2010. [Google Scholar]
- Clark, A.J.; Lake, L.W.; Patzek, T.W. Production Forecasting with Logistic Growth Models. In Proceedings of the SPE Annual Technical Conference and Exhibition, Denver, CO, USA, 30 October–2 November 2011. [Google Scholar]
- Gong, X.; Gonzalez, R.; McVay, D.A.; Hart, J.D. Bayesian Probabilistic Decline-Curve Analysis Reliably Quantifies Uncertainty in Shale-Well-Production Forecasts. SPE J.
**2014**, 19, 1047–1057. [Google Scholar] [CrossRef] - Paryani, M.; Awoleke, O.O.; Ahmadi, M.; Hanks, C.; Barry, R. Approximate Bayesian Computation for Probabilistic Decline-Curve Analysis in Unconventional Reservoirs. SPE Res. Eval. Eng.
**2017**, 20, 478–485. [Google Scholar] [CrossRef] [Green Version] - Zhang, H.; Rietz, D.; Cagle, A.; Cocco, M.; Lee, J. Extended exponential decline curve analysis. J. Nat. Gas Sci. Eng.
**2016**, 36, 402–413. [Google Scholar] [CrossRef] - Yu, S. A Comprehensive Study of b-Values for Proven Reserve Estimation Using Hyperbolic Decline for Vertical Commingled Gas Producers in Deep Basin Area of WCSB. In Proceedings of the SPE/CSUR Unconventional Resources Conference, Calgary, AB, Canada, 20–22 October 2015. [Google Scholar]
- Stumpf, T.N.; Ayala, L.F. Rigorous and Explicit Determination of Reserves and Hyperbolic Exponents in Gas-Well Decline Analysis. SPE J.
**2016**, 21, 1843–1857. [Google Scholar] [CrossRef] - Sharma, P.; Salman, M.; Reza, Z.; Kabir, C. Probing the roots of Arps hyperbolic relation and assessing variable-drive mechanisms for improved DCA. J. Pet. Sci. Eng.
**2019**, 182, 106288. [Google Scholar] [CrossRef] - Ogunyomi, B.A.; Patzek, T.W.; Lake, L.W.; Kabir, C.S. History Matching and Rate Forecasting in Unconventional Oil Reservoirs With an Approximate Analytical Solution to the Double-Porosity Model. SPE Res. Eval. Eng.
**2016**, 19, 070–082. [Google Scholar] [CrossRef] - Aybar, U.; Eshkalak, M.O.; Sepehrnoori, K.; Patzek, T.W. The effect of natural fractures closure on long-term gas production from unconventional resources. J. Nat. Gas Sci. Eng.
**2014**, 21, 1205–1213. [Google Scholar] [CrossRef] - Aybar, U.; Yu, W.; Eshkalak, M.O.; Sepehrnoori, K.; Patzek, T. Evaluation of production losses from unconventional shale reservoirs. J. Nat. Gas Sci. Eng.
**2015**, 23, 509–516. [Google Scholar] [CrossRef] - Patzek, T.W.; Male, F.; Marder, M. From the Cover: Cozzarelli Prize Winner: Gas production in the Barnett Shale obeys a simple scaling theory. Proc. Natl. Acad. Sci. USA
**2013**, 110, 19731–19736. [Google Scholar] [CrossRef] [Green Version] - Patzek, T.W.; Male, F.; Marder, M. A simple model of gas production from hydrofractured horizontal wells in shales. AAPG Bull.
**2014**, 98, 2507–2529. [Google Scholar] [CrossRef] - Eftekhari, B.; Marder, M.; Patzek, T.W. Field data provide estimates of effective permeability, fracture spacing, well drainage area and incremental production in gas shales. J. Nat. Gas Sci. Eng.
**2018**, 56, 141–151. [Google Scholar] [CrossRef] - Patzek, T.; Saputra, W.; Kirati, W.; Marder, M. Generalized Extreme Value Statistics, Physical Scaling and Forecasts of Gas Production in the Barnett Shale. Energy Fuels
**2019**, 33, 12154–12169. [Google Scholar] [CrossRef] - Patzek, T.W.; Saputra, W.; Kirati, W. A Simple Physics-Based Model Predicts Oil Production from Thousands of Horizontal Wells in Shales. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9–11 October 2017. [Google Scholar]
- Saputra, W.; Albinali, A.A. Validation of the Generalized Scaling Curve Method for EUR Prediction in Fractured Shale Oil Wells. In Proceedings of the SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition, Dammam, Saudi Arabia, 23–26 April 2018. [Google Scholar]
- Conway, J. The Weird and Wonderful Chemistry of Audioactive Decay. In Open Problems in Communication and Computation; Springer: New York, NY, USA, 1987; pp. 173–188. [Google Scholar]
- Ekhad, S.B.; Zeilberger, D. Proof of Conway’s Lost Cosmological Theorem. arXiv
**1998**, arXiv:math.CO/ math/9808077. [Google Scholar] - Finch, S.R. Mathematical Constants; Cambridge University Press: Cambridge, UK, 2003; pp. 452–454. [Google Scholar]
- Gumbel, E.J. Statistics of Extremes; Columbia University Press: New York, NY, USA, 1958. [Google Scholar]
- Saputra, W.; Kirati, W.; Patzek, T. Generalized Extreme Value Statistics, Physical Scaling and Forecasts of Oil Production in the Bakken Shale. Energies
**2019**, 12, 3641. [Google Scholar] [CrossRef] [Green Version] - Lantz, T.G.; Greene, D.T.; Eberhard, M.J.; Norrid, R.S.; Pershall, R.A. Refracture Treatments Proving Successful In Horizontal Bakken Wells. In Proceedings of the Rocky Mountain Oil & Gas Technology Symposium, Denver, CO, USA, 16–18 April 2007. [Google Scholar]
- Oruganti, Y.; Mittal, R.; McBurney, C.J.; Garza, A.R. Re-Fracturing in Eagle Ford and Bakken to Increase Reserves and Generate Incremental NPV: Field Study. In Proceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 3–5 February 2015. [Google Scholar]
- Ruhle, W. Refracturing: Empirical Results in the Bakken Formation. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, San Antonio, TX, USA, 1–3 August 2016. [Google Scholar]
- Li, C.; Han, J.; LaFollette, R.; Kotov, S. Lessons Learned From Refractured Wells: Using Data to Develop an Engineered Approach to Rejuvenation. In Proceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 9–11 February 2016. [Google Scholar]
- Gullickson, G.; Ruhle, W.; Cook, P.F. The Lexicon of Recompletion: Empirical Justification for Refrac, Reentry, or Remediation in the Bakken/Three Forks Play. In Proceedings of the SPE Western Regional Meeting, Anchorage, AK, USA, 23–26 May 2016. [Google Scholar]
- Lane, W.; Chokshi, R. Considerations for Optimizing Artificial Lift in Unconventionals. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, CO, USA, 25–27 August 2014. [Google Scholar]
- Orji, E.; Lissanon, J.; Omole, O. Sucker Rod Lift System Optimization of an Unconventional Well. In Proceedings of the SPE North America Artificial Lift Conference and Exhibition, The Woodlands, TX, USA, 25–27 October 2016. [Google Scholar]
- Oyewole, P. Artificial Lift Selection Strategy to Maximize Unconventional Oil and Gas Assets Value. In Proceedings of the SPE North America Artificial Lift Conference and Exhibition, The Woodlands, TX, USA, 25–27 October 2016. [Google Scholar]
- Sickle, S.V.; Shelly, G.; Snyder, D. Optimizing Completions and Artificial Lift in an Unconventional Play in the United States. In Proceedings of the SPE Artificial Lift Conference ó Latin America and Caribbean, Salvador, Bahia, Brazil, 27–28 May 2015. [Google Scholar]
- Male, F.; Marder, M.; Browning, J.; Gherabati, A.; Ikonnikova, S. Production Decline Analysis in the Eagle Ford. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, San Antonio, TX, USA, 1–3 August 2016. [Google Scholar]
- Male, F.; Gherabati, A.; Browning, J.R.; Marder, M. Forecasting Production From Bakken and Three Forks Wells Using a Segregated Flow Model. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, Austin, TX, USA, 24–26 July 2017. [Google Scholar]
- Kondash, A.J.; Albright, E.; Vengosh, A. Quantity of flowback and produced waters from unconventional oil and gas exploration. Sci. Total Environ.
**2017**, 574, 314–321. [Google Scholar] [CrossRef] [Green Version] - Cheng, Y. Impact of Water Dynamics in Fractures on the Performance of Hydraulically Fractured Wells in Gas-Shale Reservoirs. J. Can. Pet. Technol.
**2012**, 51, 143–151. [Google Scholar] [CrossRef] - Abualfaraj, N.; Gurian, P.L.; Olson, M.S. Characterization of Marcellus Shale Flowback Water. Environ. Eng. Sci.
**2014**, 31, 514–524. [Google Scholar] [CrossRef] - Hughes, J.D. 2016 Tight Oil Reality Check; Post Carbon Institude: Santa Rosa, CA, USA, 2016. [Google Scholar]
- Hughes, J.D. Shale Reality Check; Post Carbon Institude: Santa Rosa, CA, USA, 2018. [Google Scholar]
- Hughes, J.D. How Long Will the Shale Revolution Last?: Technology versus Geology and the Lifecycle of Shale Plays; Post Carbon Institude: Santa Rosa, CA, USA, 2019. [Google Scholar]
- Paneitz, J. Evolution of the Bakken Completions in Sanish Field, Williston Basin, North Dakota. In Proceedings of the SPE Applied Technology Workshop (ATW), Keystone, CO, USA, 6 August 2010. [Google Scholar]
- Buffington, N.; Kellner, J.; King, J.G.; David, B.L.; Demarchos, A.S.; Shepard, L.R. New Technology in the Bakken Play Increases the Number of Stages in Packer/Sleeve Completions. In Proceedings of the SPE Western Regional Meeting, Anaheim, CA, USA, 27–29 May 2010. [Google Scholar]
- Weddle, P.; Griffin, L.; Pearson, C.M. Mining the Bakken: Driving Cluster Efficiency Higher Using Particulate Diverters. In Proceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, TX, USA, 24–26 January 2017. [Google Scholar]
- Martin, E. United States Tight Oil Production 2018. Available online: https://www.allaboutshale.com/united-states-tight-oil-production-2018-emanuel-omar-martin/ (accessed on 1 September 2019).
- Ahmed, T. Reservoir Engineering Handbook: Fourth Edition; Gulf Professional Publishing: Cambridge, MA, USA, 2010; pp. 1250–1255. [Google Scholar]
- Meissner, F.F. Petroleum geology of the Bakken Formation Williston Basin, North Dakota and Montana. In 1991 Guidebook to Geology and Horizontal Drilling of the Bakken Formation; Montana Geological Society: Butte, MT, USA, 1991. [Google Scholar]
- Sonnenberg, S.A.; Pramudito, A. Petroleum geology of the giant Elm Coulee field, Williston Basin. AAPG Bull.
**2009**, 93, 1127–1153. [Google Scholar] [CrossRef] - Jin, H.; Sonnenberg, S.A. Characterization for Source Rock Potential of the Bakken Shales in the Williston Basin, North Dakota and Montana. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, CO, USA, 12–14 August 2013. [Google Scholar]
- Han, Y.; Misra, S.; Simpson, G. Dielectric dispersion log interpretation in Bakken petroleum system. In Proceedings of the SPWLA 58th Annual Logging Symposium, Oklahoma City, OK, USA, 17–21 June 2017. [Google Scholar]
- Han, Y.; Misra, S. Bakken Petroleum System Characterization Using Dielectric-Dispersion Logs. Petrophys. SPWLA J. Form. Eval. Res. Des.
**2018**, 59, 201–217. [Google Scholar] [CrossRef] - Alvarez, D.; Joseph, A.; Gulewicz, D. Optimizing Well Completions in the Canadian Bakken: Case History of Different Techniques to Achieve Full ID Wellbores. In Proceedings of the SPE Unconventional Resources Conference, Calgary, AB, Canada, 5–7 November 2013. [Google Scholar]
- LeFever, J.A. History of oil production from the Bakken Formation, North Dakota. In 1991 Guidebook to Geology and Horizontal Drilling of the Bakken Formation; Montana Geological Society: Butte, MT, USA, 1991. [Google Scholar]
- Nordeng, S.H. A brief history of oil production from the Bakken formation in the Williston Basin. Geo News
**2010**, 37, 5–9. [Google Scholar] - Kurtoglu, B. Integrated Reservoir Characterization and Modeling in Support of Enhanced Oil Recovery for Bakken; Colorado School of Mines: Golden, CO, USA, 2013. [Google Scholar]
- Tran, T.; Sinurat, P.D.; Wattenbarger, B.A. Production Characteristics of the Bakken Shale Oil. In Proceedings of the SPE Annual Technical Conference and Exhibition, Denver, CO, USA, 30 October–2 November 2011. [Google Scholar]

**Figure 1.**(

**a**) Illustration of bi-linear flow towards hydraulic fractures of a shale well. Reproduced from [28]. (

**b**) Illustration of the (almost) universal scaling curve method. The black line is the master curve that is the solution of the pressure diffusivity equation in hydrofractured well geometry. This master curve scales initially as the square root of time that later slows down due to exponentially declining rate of production. The constant C governs the vertical stretching of the master curve and can be calculated as $C={c}_{ti}/{S}_{oi}({P}_{i}-{P}_{f})$. The cumulative mass produced by individual wells is then adjusted to match the master curve by a stretching/shrinking factor of $\mathcal{M}$ along the y-axis and $\tau $ along the x-axis. Reproduced from [29].

**Figure 2.**(

**a**) The refracturing process is illustrated as an increase of the stimulated reservoir volume (SRV) from ${\mathcal{M}}_{0}$ to ${\mathcal{M}}_{1}$ at time ${t}_{1}$; and from ${\mathcal{M}}_{1}$ to ${\mathcal{M}}_{2}$ at time ${t}_{2}$. (

**b**) A modification of the physical scaling curve coupled with superposition solves well refracturing problem. If primary production before refracturing has the recovery constant C (cf. Figure 1), then each refracturing event at ${t}_{j}$ will start an imaginary well with the recovery constants $C{a}_{j}$. Here ${a}_{j}$ scales the effectiveness of each fracturing job relative to the initial mass in place (${a}_{j}=({\mathcal{M}}_{j}-{\mathcal{M}}_{j-1})/{\mathcal{M}}_{0}$). Finally, the total master curve is scaled as ${C}_{T}=C(1+{a}_{1}+\dots +{a}_{n})$ to match the discontinuous historical production.

**Figure 3.**(

**a**) The probability density function (PDF) and (

**b**) the cumulative distribution function (CDF) of oil rate for the Bakken wells after 12 months on production. The field data were fit with the generalized extreme value (GEV) distribution function that perfectly matches the experimental probability distributions. The ${P}_{50}$ well is the expected value of the distribution, the ${P}_{10}$ well is exceeded by only 10% of wells, and the ${P}_{90}$ well is exceeded by 90% of wells.

**Figure 4.**Daily oil rates and cumulative oil for the 14,888 horizontal oil wells in the Middle Bakken (9894) and the Upper Three Forks (4994).

**Figure 5.**4845 horizontal oil wells: (

**a**) 3349 in the Middle Bakken and (

**b**) 1496 in the Three Forks are categorized as non-interfering wells, because their cumulative production is still growing linearly versus the square root of time, an indication of a transient flow regime. From the 2-D histograms of scaling parameters, the expected values of ${t}_{max}$ and $\mathcal{K}\sqrt{{t}_{max}}$ are 75 months and 30 ktons, respectively, for the Middle Bakken, and 65 months and 27 ktons for the Three Forks.

**Figure 6.**6401 horizontal oil wells: (

**a**) 4245 in the Middle Bakken and (

**b**) 2156 and the Three Forks are categorized as interfering wells. These wells are subject to pressure interference between consecutive hydrofractures. In other words, oil production from these wells is in a pseudo-steady state flow regime, and the oil rate is expected to decline exponentially. The expected values of $\tau $ and $\mathcal{M}$ from the 2-D histograms are, respectively, 100 months and 420 ktons for the Middle Bakken, and 90 months and 320 ktons for the Upper Three Forks.

**Figure 7.**2363 wells cannot be matched with the interfering or non-interfering segments of the scaling curve. The poor matches are caused by multiple production jumps that may be due to refracturing of the old wells. Thus, this group of wells is matched differently with the modified physical scaling curve detailed in Figure 2. The two example wells in (

**a**,

**b**) are completed in the Middle Bakken formation, while the other two in (

**c**,

**d**) are completed in the Three Forks formation. These examples demonstrate the robustness of the modified scaling curves. The values of a’s may reflect the effectiveness of each refracturing job (or a change in the well operating conditions).

**Figure 8.**Different classes of the 14,888 horizontal wells in the Middle Bakken and Upper Three Forks. There are 6401 interfering wells, 4845 non-interfering wells, 2363 “refrac” wells, and 1279 new wells that have less than 12 months on production. The filled circles show the surface locations of active wells in each class, while the empty circles denote inactive wells.

**Figure 9.**Historical production data and the physical scaling projection for all horizontal wells in the Middle Bakken and Upper Three Forks. To match historical oil rate and cumulative oil in the Bakken formation, all individual scaling curves for the 14,888 wells are summed up vs. calendar time.

**Figure 10.**(

**a**) Matches of oil production rate (black) of a single well in the Bakken shale with our physical scaling method (blue) and hyperbolic decline curve (red). The algorithm used for the hyperbolic DCA is based on the Reservoir Engineering Handbook (Fourth Edition), 2010 by Tarek Ahmed. There seems to be little discrepancy between these two methods. (

**b**) The oil rate forecasts in panel (

**a**) are integrated in time to obtain cumulative oil. The physical scaling and hyperbolic DCA curves differ significantly. (

**c**,

**d**) show the quality of individual matches of 11,246 non-refractured wells in the Bakken. Overall, our physical scaling matches the actual annual production better than the hyperbolic DCA (according to the R

^{2}values). Individual matches of all wells in the Bakken with both methods are stacked up to reconstruct the past total field oil rate (

**e**) and cumulative production (

**f**). The physical scaling traces perfectly historical production. In contrast, the hyperbolic DCA systematically overestimates the field EUR, yielding 1 billion m

^{3}(6.5 billion bbl), an estimate that is 45% higher than that obtained with physical scaling.

**Figure 11.**The stacked bars show the numbers of existing wells from the DrillingInfo dataset in 2019, and the potential wells from the EIA report [6] in each Bakken TPS assessment unit mapped onto the corresponding counties in the Middle Bakken and Upper Three Forks Formations. The lines show the corresponding EUR values from the physical scaling and the EIA statistical predictions. The ${P}_{10}$, ${P}_{50}$, and ${P}_{90}$ wells were obtained by applying the generalized extreme value (GEV) distribution for each set of EURs from the scaling curve method in each sub-region [34]. The two-letter codes abbreviate the five Bakken assessment units detailed in Appendix A: Central Basin (CB), Eastern Transitional (ET), Nesson–Little Knife (NL), and Northwest Transitional (NT).

**Figure 12.**A map of EURs obtained from the universal scaling curve method for 14,888 horizontal wells in Bakken shale. Notice that this map resembles the water cut map, rather than the GOR map. This indicates that EUR is negatively correlated with water cut.

**Figure 13.**Scatter plot of EURs vs. oil cut (

**a**) and EUR vs. lateral length (

**b**) for all 14,888 horizontal oil wells in Bakken. The shorter pre-2010 wells are colored in red.

**Figure 14.**(

**a**) Average pressure interference time, $\tau $ in months vs. calendar time for the Middle Bakken and Upper Three Forks. (

**b**) Average lateral length vs. calendar time shows that old wells have short laterals averaging 1.5 km (5000 ft), while the recent wells are longer at about 3 km (10,000 ft). (

**c**) Average gas–oil ratio (GOR) vs. calendar time shows a positive trend for both Middle Bakken and Upper Three Forks. (

**d**) Average water cut vs. calendar time also shows a positive trend for the Middle Bakken and Upper Three Forks.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Saputra, W.; Kirati, W.; Patzek, T.
Physical Scaling of Oil Production Rates and Ultimate Recovery from All Horizontal Wells in the Bakken Shale. *Energies* **2020**, *13*, 2052.
https://doi.org/10.3390/en13082052

**AMA Style**

Saputra W, Kirati W, Patzek T.
Physical Scaling of Oil Production Rates and Ultimate Recovery from All Horizontal Wells in the Bakken Shale. *Energies*. 2020; 13(8):2052.
https://doi.org/10.3390/en13082052

**Chicago/Turabian Style**

Saputra, Wardana, Wissem Kirati, and Tadeusz Patzek.
2020. "Physical Scaling of Oil Production Rates and Ultimate Recovery from All Horizontal Wells in the Bakken Shale" *Energies* 13, no. 8: 2052.
https://doi.org/10.3390/en13082052